How many gram ions of `SO_(4)^(-2)` are present in 1 gram molecule of` K_(2)SO_(4). Al_(2)(SO_(4))_(3).24H_(2)O`?

Options

A. 2
B. 3
C. 1
D. 4

Explanation

To determine how many gram ions of \( SO_4^{2-} \) are present in 1 gram molecule of \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \), we can follow these steps:

### Step 1: Identify the formula and components
The compound given is \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \). This is known as potash alum.

### Step 2: Calculate the molar mass of the compound
To find the molar mass of \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \), we will calculate the individual molar masses of each component:

- Molar mass of \( K_2SO_4 \):
- Potassium (K): \( 39.1 \, \text{g/mol} \times 2 = 78.2 \, \text{g/mol} \)
- Sulfate (SO4): \( 32.1 \, \text{g/mol} + 16 \times 4 = 96.1 \, \text{g/mol} \)
- Total for \( K_2SO_4 = 78.2 + 96.1 = 174.3 \, \text{g/mol} \)

- Molar mass of \( Al_2(SO_4)_3 \):
- Aluminum (Al): \( 26.98 \, \text{g/mol} \times 2 = 53.96 \, \text{g/mol} \)
- Sulfate (SO4): \( 32.1 \, \text{g/mol} + 16 \times 4 = 96.1 \, \text{g/mol} \), and there are 3 sulfate ions
- Total for \( Al_2(SO_4)_3 = 53.96 + (3 \times 96.1) = 53.96 + 288.3 = 342.26 \, \text{g/mol} \)

- Molar mass of \( 24H_2O \):
- Water (H2O): \( 18.02 \, \text{g/mol} \times 24 = 432.48 \, \text{g/mol} \)

Now, add all these together:
\[ \text{Total molar mass} = 174.3 + 342.26 + 432.48 = 949.04 \, \text{g/mol} \]

### Step 3: Determine the number of sulfate ions in the compound
From the formula \( K_2SO_4 \cdot Al_2(SO_4)_3 \):
- \( K_2SO_4 \) contributes 1 sulfate ion.
- \( Al_2(SO_4)_3 \) contributes 3 sulfate ions.

Thus, the total number of sulfate ions in the compound is:
\[ 1 + 3 = 4 \, \text{sulfate ions} \]

### Step 4: Calculate the number of gram ions of \( SO_4^{2-} \)
Since 1 mole of the compound contains 4 moles of \( SO_4^{2-} \), we can say that 1 gram molecule of the compound contains 4 gram ions of \( SO_4^{2-} \).

### Final Answer
Therefore, there are **4 gram ions of \( SO_4^{2-} \)** present in 1 gram molecule of \( K_2SO_4 \cdot Al_2(SO_4)_3 \cdot 24H_2O \).

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